A pharmaceutical manufacturer is concerned that the impurity concentration in pills does not exceed 4%. It is known that from a particular production run, impurity concentrations follow a normal distribution with standard deviation 0.8%. A random sample of 100 pills from a production line was checked, and the sample mean impurity concentration was 4.12%. (a) Test the null hypothesis that the population mean impurity concentration is 4% against the alternative that it is greater than 4%. The significance level of this test is 5% (b) Find the power of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 4.3%.